Monotone Global Games

Hoffmann, Eric and Sabarwal, Tarun (2018): Monotone Global Games.

Abstract

We extend the global games method to finite player, finite action, monotone games. These games include games with strategic complements, games with strategic substitutes, and arbitrary combinations of the two. Our result is based on common order properties present in both strategic complements and substitutes, the notion of p-dominance, and the use of dominance solvability as the solution concept. In addition to being closer to the original arguments in Carlsson and van Damme (1993), our approach requires fewer additional assumptions. In particular, we require only one dominance region, and no assumptions on state monotonicity, or aggregative structure, or overlapping dominance regions. As expected, the p-dominance condition becomes more restrictive as the number of players increases. In cases where the probabilistic burden in belief formation may be reduced, the p-dominance condition may be relaxed as well. We present some examples that are not covered by existing results.

• Item Type: MPRA Paper
• Language: English
• Keywords: Global games, strategic complements, strategic substitutes, monotone games, equilibrium selection
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Baliga, S., and T. Sjostrom (2012): “The Strategy of Manipulating Conflict,” American Economic Review, 102, 2897–2922

Basteck, C., T. R. Dani¨els, and F. Heinemann (2013): “Characterising equilibrium selection in global games with strategic complementarities,” Journal of Economic Theory, 148(6), 2620–2637

Carlsson, H., and E. van Damme (1993): “Global Games and Equilibrium Selection,” Econometrica, 61(5), 989–1018

Frankel, D. M., S. Morris, and A. Pauzner (2003): “Equilibrium selection in global games with strategic complementarities,” Journal of Economic Theory, 108(1), 1–44

Harrison, R., and P. Jara-Moroni (2016): “Equilibrium selection in global games with strategic substitutes,” Working paper

Healy, P. J. (2007): “Group reputations, stereotypes, and cooperation in a repeated labor market,” American Economic Review, 97(5), 1751–1773

Kajii, A., and S. Morris (1997): “The Robustness of Equilibria to Incomplete Information,” Econometrica, 65(6), 1283–1309

Keser, C., I. Suleymanova, and C. Wey (2012): “Technology adoption in markets with network effects: Theory and experimental evidence,” Information Economics and Policy, 24(3-4), 262–276

Kilgour, D. M., and F. C. Zagare (1991): “Credibility, uncertainty, and deterrence,” American Journal of Political Science, 35(2), 305–334

Macrae, C. N., and G. V. Bodenhausen (2000): “Social cognition: Thinking categorically about others,” Annual Review of Psychology, 51(1), 93–120

Morris, S., R. Rob, and H. S. Shin (1995): “p-Dominance and Belief Potential,” Econometrica, 63(1), 145–157

Morris, S., and H. S. Shin (2005): “Notes on strategic substitutes and complements in global games,” Available online at author’s website

Weinstein, J., and M. Yildiz (2007): “A structure theorem for rationalizability with application to robust predictions of refinements,” Econometrica, 75(2), 365–400